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IC 


8992 



Bureau of Mines Information Circular/1984 



Use of Steel Sets in Underground Coal 



By J. H. Steers, M. O. Serbousek, and K. E. Hay 




UNITED STATES DEPARTMENT OF THE INTERIOR 



Information Circular 8992 ^-r- 

Use of Steel Sets in Underground Coal 



By J. H. Stears. M. O. Serbousek, and K. E. Hay 




UNITED STATES DEPARTMENT OF THE INTERIOR 
William P. Clark, Secretary 

BUREAU OF MINES 
Robert C. Horton, Director 




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Library of Congress Cataloging in Publication Data: 



Stears, J. H. (Juel H.) 

Use of steel sets in underground coal. 

(Information circular / United States Department of the Interior, 
Bureau of Mines ; 8992) 

Bibliography: p. 15. 

Supt. of Docs, no.: I 28.27:8992. 

1. Mine timbering. 2. Ground control (Mining). I. Serbousek, M. 
O. (Maynard O.). II. Hay, K. E. (Kenneth E.). III. Series: Informa- 
tion circular (United States. Bureau of Mines) ; 8992. 



'¥m^%^iA [TN289] 622s [622'.334] 84-600202 



CONTENTS 

Page 

Abstract. 

Introduction 

Steel support accidents 

Survey of current practices 

Steel support systems 

Steel crossbars 

Rigid steel arches 

Yielding steel arches 

Background information for design of steel supports 

Types of roof strata 

Overburden pressure 

Seam thickness 

Immediate roof type 

Floor type 

Ent ry vd.d th 

Entry shape 

Rock properties 

Rock mechanics data 

Steel type : 

Backpacking 

Expeditious support installation 

Example of steel support selection for U.S. mines 

Load determination 

Support selection 

Checks for support adequacy 

Shear capacity 

Lateral stability 

Deflection 

Localized flange or web buckling 

Support length (web crippling) 

Summa ry 

References 

Appendix. — Explanation of symbols 

ILLUSTRATIONS 

1. Steel arch configurations 3 

2. Arch-member cross sections 4 

3. Types of bolted joints 4 

4. Butt plate joint 4 

5. Typical yielding arch shapes 6 

6. Yield box construction 7 

7. Typical arch with U-shaped cross section 7 

8. Examples of poor and good backpacking practices 9 

9. Possible roof support envelopes for entry width 10 

10. Nomogram for determining support loads 11 

11. Types of beam loading conditions 12 

12. Pertinent properties for selected beam 13 

TABLE 
1. Summary of accidents involving steel support members 2 



1 


1 


2 


2 


3 


3 


3 


5 


6 


7 


8 


8 


8 


8 


8 


8 


8 


8 


9 


9 


9 


10 


10 


11 


12 


12 


13 


13 


13 


14 


14 


15 


16 





UNIT OF MEASURE 


ABBREVIATIONS USED 


IN THIS REPORT 


ft 


foot 


lb 


pound 


ft-lb 


foot pound 


lb/ft 


pound per foot 


h 


hour 


lb/ft3 


pound per cubic foot 


in 


inch 


pet 


percent 


in3 


cubic inch 


psi 


pound per square inch 


kips 


thousand pound 


yr 


year 



USE OF STEEL SETS IN UNDERGROUND COAL 

By J. H. Stears, ^ M. 0. Serbousek,^ and K. E. Hay^ 



ABSTRACT 

This Bureau of Mines report presents information on the use of steel 
supports in U.S. coal mines, including accident statistics for a 3-yr 
period and a survey of present applications and problems. It also con- 
tains a summary of available steel arch configurations and a descrip- 
tion of steel support design criteria for ground control applications. 

INTRODUCTION 

A primary goal of Bureau of Mines research is to provide better roof 
control and thus reduce the exposure of miners to falls of roof rock. 
Much of the coal lying under easily supported roof has already been 
mined. As mining progresses into deeper coal seams and poorer roof 
areas, ground control will become more difficult, and accidents result- 
ing from roof falls can be expected to increase. Steel beams and rails 
are widely used in the mining industry to support difficult ground. 
Steel arches, which are slowly gaining acceptance in U.S. mines, are 
the most successful devices for ground control in poor conditions. 

Numerous accidents occur while handling and installing steel sup- 
ports. It is likely that accidents will increase with expected in- 
creased use of steel for support. Some of the safety problems appear 
to involve failure to use adequate design criteria already available. 

This report presents information on the use and application of steel 
supports in U.S. coal mines. It includes accident statistics associ- 
ated with the use of steel supports for a 3-yr period, a survey of coal 
mining companies for applications and problems associated with the use 
of steel supports, a description of the various arch configurations 
available, and a presentation of steel support design criteria. 



Mining engineer. 
^Structural engineer. 
-^Supervisory civil engineer. 

Spokane Research Center, Bureau of Mines, Spokane, WA. 



STEEL SUPPORT ACCIDENTS 



Steel support accidents are summarized 
in table 1 for 1978-80. These data were 
obtained by searching through the acci- 
dent files for the period covered; some 
accidents may have been missed owing to 
classification and filing procedures. 

TABLE 1, - Summary of accidents involving 
steel support members 



Category 


1978 


19 79 


1980 


Total 


Transportation. . 


28 


34 


17 


79 


Installing: 










Handling 


7 


18 


8 


33 


Beam slipped 










and fell 


1 


2 


2 


5 


Recovering 





1 


1 


2 


Total 


36 


55 


28 


119 



The first category listed is the trans- 
porting of steel members. This includes 
loading, unloading, moving, lifting, or 
carrying supports. The injuries include 
such items as mashed and cut fingers and 
toes , mashed hands , bruises to various 



parts of the body, and sprained muscles 
in the neck, shoulder, back, abdomen, and 
legs. Generally, the weight and awkward- 
ness of the beams create difficulties in 
handling in tight quarters. 

The second category is installing sup- 
ports. Most of the accidents occurred 
while handling the beams during installa- 
tion. They include mashed, cut, bruised, 
or sprained muscles that occurred while 
moving the beams into position. Some of 
the beams were being manually lifted into 
position against the roof, while others 
were being placed on machine booms for 
subsequent lifting into position. A few 
accidents occurred when beams slipped and 
fell off the jacks or machine booms while 
being lifted into position. 

In the third category of recovering 
members , only one accident occurred in 
19 79 and one in 1980. They involved a 
sprained shoulder muscle and a mashed 
hand. 



SURVEY OF CURRENT PRACTICES 



A limited survey of selected coal min- 
ing companies using steel supports was 
made to obtain information on pertinent 
practices and problems. Five companies 
operating 17 mines were contacted. The 
companies were located in central and 
southeastern Pennsylvania, northern West 
Virginia, and western Virginia. 

Steel supports were used in supporting 
haulageways , ventilation overcasts, and 
roof -fall areas. They were also used in 
longwall entries and faces and as airway 
supports. Steel beams ranging in size 
from 4 to 8 in and steel rails ranging in 
size from 60 to 120 lb were employed. 
Both yielding and rigid arches were used, 
with 4 in being the predominant size. 
One company covered its 4-in arches with 
corrugated steel tunnel liner. 

Steel supports were installed both man- 
ually and with equipment. Manual instal- 
lation involves jacking the supports 



against the roof with a beam jack. Roof- 
bolting machines equipped with timber 
booms were used to lift the supports 
against the roof. Equipment for holding 
the supports in position until legs are 
installed include beam jacks, hydraulic 
jacks, and roof -bolted saddles. None of 
the companies presently recover any steel 
supports. Care is taken to install the 
horizontal beams level and the support 
posts plumb. The support posts were 
firmly wedged under the beams, and any 
voids above the beam were blocked to pro- 
vide support against the roof. 

Handling of steel supports was a ma- 
jor problem. This operation is difficult 
and hazardous due to the size, weight, 
and bulkiness of the supports. All com- 
panies indicated that most of their in- 
juries occurred while handling supports. 
Strains to various muscles occurred when 
lifting and moving the heavy beams and 
rails. Mashed fingers and hands that 



were caught between the support being 
handled and another object were especial- 
ly prevalent. Foot injuries from fall- 
ing supports were also quite conunon. 
Another major problem was the excessive 
time required for the installation of 
steel supports. 

Various modes of support failure were 
reported. These include bending failure 
of beams, shearing and twisting failure 
of steel rails, and compression failure 



of the supporting legs. Footing failures 
in fire clay bottom were also reported. 

Two companies commented on possible re- 
search needs. One company mentioned that 
safe and timely installation of the heavy 
steel supports in the confining mine en- 
vironment remains the greatest obstacle. 
Another company suggested further inves- 
tigation of resupporting roof-fall cavi- 
ties with arch supports and corrugated 
steel tunnel liner. 



STEEL SUPPORT SYSTEMS 



Much of the following information on 
steel support systems is based on litera- 
ture from Bethlehem Steel,'* Commercial 
Shearing, Inc., and the Dosco Corp. 

STEEL CROSSBARS 

Steel crossbars are the most common 
steel support. They are usually adequate 
for fairly heavy loads. However, they 
are inadequate in extreme situations such 
as massive fall areas or excessively 
squeezing ground conditions. Heavy loads 
will create excessive bending and even- 
tual failure of the beams. Wide-flange 
or H-sections are preferred because of 
their greater resistance to bending. 
Steel rails are also used as crossbars. 
However, old rails may have lost ductil- 
ity and, consequently, may be susceptible 
to catastrophic failure. 

RIGID STEEL ARCHES 

Rigid arches are designed to support 
without yielding. The arch is more effi- 
cient than the flat crossbar. Depending 
on the shape and loading conditions of 
the arch, the imposed load in the arch is 
transmitted as compression rather than 
bending forces. 

A variety of configurations can be sup- 
plied by the different companies. Some 
of the standard ones are shown in figure 

'^Reference to specific products or man- 
ufacturers does not imply endorsement by 
the Bureau of Mines. 



1. These include the two- and three- 
piece continuous arch and the two-piece 
rib-and-post. Flat-top arches with ei- 
ther straight or curved sides are also 
available. In mines with a swelling bot- 
tom, invert-strut arches are recommended. 
Almost any desired conf igiiration for dif- 
fering ground conditions can be supplied 
on special order. 

Arch members with wide-flange beam 
cross sections are available, as shown in 
figure 2A, However, this cross section 




2-piece continuous arch 




3-piece continuous arch 





2-piece rib andpost Flat lop with straight sides 




Flat top wrih curved sides 



Invert strut 



FIGURE 1. - Steel arch configurations. 



is relat 
forces 
twisted 
steel jo 
section) 
able (f 
similar 
and , in 



ively weak in resisting oblique 

and is susceptible to being 

out of shape by them. Rolled 

ist (American standard beam or S 

cross sections are also avail- 

ig. 2S), These offer properties 

to those of the wide-flange beams 

addition, are two to three times 



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/ 
/ 
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/ 



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arTihrm. (rm/nrTY^^^^^^'::^ 



A B C 

FIGURE 2. « Arch-member cross sections. A, 
Wide-flange beam; B, rolled steel joist; C, box 
sections. 




stronger under oblique loadings. Box- 
section beams (fig. 2C) are two shapes 
continually seam-welded. They give bet- 
ter all-round performance under heavy 
loading than the rolled-joist sections. 

Connectors are necessary in most arches 
since effective one-piece units cannot be 
transported underground. Joining of the 
arch sections is done in a variety of 
ways. One type of joint is shown in fig- 
ure 3j4 . A single bolt holds the two 
forged lugs tightly together to form a 
rigid joint and transmit shear forces and 
bending moment from one member to the 
other. 

A flexible joint is shown in figure 3B. 
A single bolt holds two rounded forged 
lugs together which roll on themselves 
under weight, thus enabling the joint to 
rotate under load without fracturing. 

Another vender uses butt plates welded 
to the beam ends (fig. 4). The beam ends 
are butted together and connected with 
bolts through holes provided in the 
plates. 

Arches are usually installed on 3- to 
6-f t centers , and they are connected to- 
gether with tie rods for lateral sta- 
bility. Normally, the periphery of the 
arches is lagged with 2- to 3-in treated 
wooden boards. 




B 

FIGURE 3. - Types of bolted joints. A, 
Rigid joint; B, flexible joint. 



For maximum efficiency, the void space 
between the outside of the arches and the 
strata must be backfilled or solidly 
blocked. This provides uniform loading 
of the arch structure and avoids point 
loading that would locally overstress the 
arches and destroy the overall support 
capacity of the total arch. Rigid arches 




FIGURE 4. - Butt plate joint. 



are usually installed on main haul- 
ageways, slopes, and shaft stations that 
require permanent support where large 
ground movements are not expected. 

YIELDING STEEL ARCHES 

Yielding mine arches consist of arch 
or ring sets that incorporate a sliding 
friction assembly to accommodate heavy 
ground pressure and thus prevent distor- 
tion of the support. 

The yielding arch is designed to relax 
before it becomes excessively bent or 
distorted. The joint acts as a safety 
valve to keep the steel set from being 
destroyed; it is designed to yield at a 
load below the yield point of the steel. 

Yielding arches serve the same function 
as rigid arches but are much more ef- 
fective in areas of severe pressures or 
squeezing ground conditions, which pro- 
duce large deformation that would destroy 
a rigid arch. They are an economical 
support method under severe conditions 
where extensive movements occur because 
of faulted ground, overstressed strata, 
longwall operations, or strata with vari- 
able properties. 

Yielding arches are fabricated in vari- 
ous shapes such as circular and horseshoe 
and consist of three or more segments of 
high-strength steel with a yield point 
above 50,000 psi. Three typical arch 
shapes are shown in figure 5. The three- 
segment symmetrical arch with leg seg- 
ments toed in (fig. 5A) is used where the 
ground pressure is predominantly verti- 
cal, the three-segment symmetrical arch 
with leg segments toed out (fig. 5B) re- 
sists lateral as well as vertical ground 
pressures, and the symmetrical ring (fig. 
5C) resists ground pressures from all 
directions. 

The two most common yielding mechanisms 
are the yield box and the overlap joint. 
The yield box was developed for use 
with standard-type beam sections such as 



the wide-flange, joist, and box-section 
beams. The yield box is placed on the 
floor, and the lower end of the arch leg 
is inserted into its top. Construction 
of a yield box is shown in figure 6. 
When the support is set, frictional re- 
sistance is established between the arch 
leg, the wooden wedge, the brake shoe, 
and the rear side of the box. 

Several companies furnish arches made 
of U-shaped cross sections that nest to- 
gether at the ends to form an overlapping 
joint. Heavy U-bolt clamps are installed 
over the joints to provide the yielding 
feature. The joints are tightened enough 
to hold under normal loads, but when ex- 
cessive pressures develop, they permit 
the nested segments to slide or yield be- 
fore the yield strength of the steel is 
reached. This relieves the load and 
maintains the structural integrity of the 
arch while the ground is permitted to 
relax gradually until equilibrium is 
reached. As the successful functioning 
of a yielding set depends on its ability 
to yield when required, it is critical 
that the U-bolts at the joints be proper- 
ly tightened. The U-bolt nuts are usu- 
ally torqued to between 150 and 180 ft-lb 
(J,, p. 406). 5 

Views of a typical arch and the 
U-shaped cross section are shown in 
figure 7. The most commonly used sec- 
tions weigh from 10 to 25 lb/ft and have 
outside dimensions of 3 to 7 in. Moduli 
of sections on "XX" and "YY" axes are 
practically equal, thereby offering uni- 
form resistance to eccentric loading. 
Ordinary H-beams give poor support when 
loads are applied at an angle to the 
major axis of inertia, causing torsional 
moment on the section. The high torsion- 
al resistance of the U-shaped sections 
allows them to be twisted out of the ver- 
tical plane and still provide adequate 
strength. 

^Underlined numbers in parentheses re- 
fer to items in the list of references 
preceding the appendix. 



Arches are spaced at 2- to 5-ft inter- 
vals , depending on expected ground pres- 
sure. Adjoining sets are connected with 
horizontal struts made of steel channels, 
pipes , or rods to maintain spacing and 
provide lateral stability. Treated tim- 
ber lagging is installed around the 



outside of the arches, and blocking or 
backfilling is used to provide uniform 
loading. Footers of steel plate, channel 
steel, or wood blocks are placed between 
the bottom of the legs and the floor to 
reduce penetration if the floor is soft. 



BACKGROUND INFORMATION FOR DESIGN OF STEEL SUPPORTS 



This section was extracted from "Steel 
Supports Design Criteria: A Summary of 
European Data" (2^) . This Bureau contract 
report presents information pertaining to 
the relationship between steel support 



selection and the physical and geological 
parameters that make up the support envi- 
ronment. The following parameters were 
examined to determine their contribution 
to support design. 





B 




FIGURE 5. - Typical yielding arch shapes. A, Three-segment symmetrical with legs toed 
in; B, three-segment symmetrical with legs toed out; C, symmetrical ring. 



Arch leg 



Wooden' 
wedge 




U-bolt 



Brake shoe 




Rear side 
of box 



FIGURE 6. - Yield box construction. 

TYPES OF ROOF STRATA 

The roof strata in underground coal 
mines are normally divided into three 
classes: immediate roof, main roof, and 
total remaining overburden. The immedi- 
ate roof is that portion of the strata 
immediately above the mined opening that 
will fall if left unsupported for a rela- 
tively short period (usually a few days). 
The behavior of the immediate roof is 
highly dependent on opening width, in 
situ stresses, induced mining stresses. 




Arch profile 




Cross section 

FIGURE 7. - Typical arch with U-shaped cross 
section. 

structure, and environmental factors such 
as temperature and moisture. The immedi- 
ate roof is of the most direct concern 
for safety in the mined opening and, 
therefore, is the stratum toward which 
the most control efforts have been di- 
rected. The two basic methods of control 
that can be applied to the immediate roof 
are internal, such as rock bolts, and ex- 
ternal, such as steel supports. 

The second class of roof strata is the 
main roof. This is the stratum that lies 
above the immediate roof and spans the 
opening if the immediate roof falls. It 
is generally agreed in the mining indus- 
try that the main roof cannot be sup- 
ported by artificial means. This means 
that roof bolts, cribs, steel supports, 
etc. , will not be effective in supporting 
the main roof. 



The third strata classification is the 
total remaining overburden. This over- 
burden will settle, but normally this 
settlement can be postponed long enough 
to permit mining; its stability depends 
upon the action of the main roof. 

In multiple-seam mining, pillar rem- 
nants in overlying seams may cause 
large stress concentrations. The entries 
should be aligned, as much as possi- 
ble, to provide more uniform stress 
conditions, 

OVERBURDEN PRESSURE 

Overburden pressure does not have a di- 
rect effect on the selection of a steel 
support design. However, the overburden 
pressure does have an indirect effect in 
the following ways: 

1, The overburden pressure is one of 
the factors that determine the amount of 
convergence that can be expected in an 
opening and, hence, the amount of defor- 
mation that the support can be expected 
to receive, 

2, The overburden pressure also af- 
fects the stress in the immediate roof 
that will comprise the support load. The 
overburden pressure is one of the factors 
that determine the height of the expected 
support envelope. 

SEAM THICKNESS 

The seam thickness enters into support 
selection both directly and indirectly. 
Directly, the seam thickness determines 
the height of the openings and supports 
and, therefore, the resistance of the 
supports to column failure. Indirectly, 
the seam thickness is one of the factors 
in determining of convergence and, there- 
fore, in determining the amount of ex- 
pected deformation, 

IMMEDIATE ROOF TYPE 

The immediate roof type is the single 
most important factor in determining 



steel support design. The immediate 
roof's weight, thickness, stress, and 
competence all influence the design of 
the support. The immediate roof is the 
strata that are actually being supported 
by the steel supports and, therefore, its 
properties are vital, 

FLOOR TYPE 

The type of floor is one of the con- 
tributors of the convergence and, hence, 
the expected deformation. Since the sup- 
port normally rests on the floor, the 
floor type also determines the need for 
footpads or other load-spreading devices. 

ENTRY WIDTH 

Support design is directly dependent on 
entry width in two ways. First, sup- 
ported load is directly proportional 
to width. Second, support design and 
strength are directly proportional to 
span. 

ENTRY SHAPE 

Entry shape (rectangular, arched, full 
circle, etc.) has a significant effect on 
the stability of the opening. It also 
affects the amount of artificial suupport 
required, 

ROCK PROPERTIES 

Strength parameters for the strata 
around the opening should be determined. 
Although the strength of coal does not 
directly enter into any of the design in- 
formation, it does affect convergence and 
expected deformation. Convergence is in- 
fluenced by the mechanical strength of 
the materials in the main roof , immediate 
roof, coal seam, and floor, 

ROCK MECHANICS DATA 

The height and shape of the support 
envelope that the structure must be de- 
signed for are determined by the height 
and integrity of the pressure arch that 
will form (assuming laminated strata) 
when the entry material is removed. 



STEEL TYPE 

Mild steel (grade 40 to 60) with good 
ductility is desirable for underground 
use. The ductility of the steel de- 
termines its ability to accept localized 
yielding without catastrophic failure 
of the support. Surface hardness is im- 
portant for yielding arches to ensure 
that sliding movement can still take 
place under load without gouging of the 
sliding surfaces. Detailed discussions 
of steel for use in underground sup- 
ports can be found in chapter 5 of Fritz 
Spruth's book, "Steel Roadway Supports" 
(_3) , and in chapter 2 of Proctor and 
White's book, Rock Tunneling With Steel 
Supports" (^) . Available standard U.S. 
steel sections are listed in the manual 
of steel construction (_5) by the Amer- 
ican Institute of Steel Construction 
(AISC). This manual also includes design 
and fabrication procedures for several 
grades of steel. The allowable stresses 
listed in the manual can be increased 
to the yield point of the steel for 
underground temporary support. Several 
good textbooks covering elastic and plas- 
tic steel design procedures are avail- 
able (^~8^) • They cover the principles 
of good steel design which account for 
bending, axial, torsion, and shear 
stresses, safety factors, axial and lat- 
eral buckling, shear stiffness, end bear- 
ing, etc. 

BACKPACKING 

Most steel support failures occur from 
point loads that overstress the support 
locally. Failure in this context means 
failure of the steel support to maintain 
entry shape because of local deformation. 
To prevent this type of failure, attempts 
are made to provide a continuous struc- 
tural interconnection between the support 
and the surrounding rock. In practice, 
this is accomplished in two steps. 

First, considerable care is taken to 
cut the entry to the approximate shape 
of the support. This avoids the need 
to fill large openings, which is costly. 
Also, large openings are difficult to 
fill with a material that will evenly 



distribute the load from the surrounding 
strata. Figure 8 shows examples of poor 
and good practices. 

Second, when the support is set, the 
space between the support and the sur- 
rounding rock is packed with a material 
that is deforraable and yet has the struc- 
tural integrity necessary to transfer the 
load from the surrounding strata. A com- 
mon material used is waste rock. In 
British mines, the waste rock is placed 
in paper bags, and the bags are then 
packed into the space. The small size 
of the rock and the use of bags make 
the material handleable and yet give 
it the needed properties of deformation 
and integrity. The most common material 
used in U.S. mines is wood because of its 
availability. 

EXPEDITIOUS SUPPORT INSTALLATION 

Steel supports should be installed 
closely behind the face to minimize the 
span of unsupported roof and the time 
that a section of roof remains unsup- 
ported. European practice is to install 
steel arches within about 6 ft of the 
face and within 8 h after roof exposure. 





D hu n n II n nnn 



nnnnnunniin armr 

n n I 1 u u g y u a_Q.jafl_XL 





Poor practice Overcutting requires 
excessive timbering 




Good practice Close cutting requires 
minimal amount of blocking 

FIGURE 8. - Examples of poor and good back- 
packing practices. 



10 



EXAMPLE OF STEEL SUPPORT SELECTION FOR U.S. MINES 



The following example describes a two- 
step process for the design of steel sup- 
ports using available U.S. steel sec- 
tions. The two steps involved are load 
determination and support selection. 

LOAD DETERMINATION 

First, it is necessary to determine the 
expected loads and the support required 
for those loads. The analysis is based 
on the immediate roof envelope. Figure 9 
shows three roof envelopes at heights of 
b/2, b, and 3b/2 above the roof line. It 
is assumed that the envelope acts as a 
free surface (that is, the rock above the 
envelope is self-supporting and no loads 
are transferred from the surrounding 
strata). The heights of the roof enve- 
lopes shown in figure 9 are idealizations 
that include conditions normally encoun- 
tered in practice. The actual height of 
the envelope in a particular mine may be 
less or greater than those depicted. 

The shape of the roof envelope is con- 
sidered to be a parabola. Assuming a 




Height to 

3b/2 

envelope 



Height to 

b 

envelope 



Height to 

b/2 

envelope 



FIGURE 9. - Possible roof support envelopes 
for entry width. 



parabolic roof envelope at a height of h 
ft in the roof above an entry b ft wide, 
the area of the parabola between the roof 
line and the envelope is 



A = 2/3 bh. 



(1) 



Multiplying by a distance of 1 ft along 
the entry gives the volume of rock be- 
tween the roof line and the envelope. 



V = 2/3 bhl. 



(2) 



Multiplying by y (the density of the rock 
in pounds per cubic feet) gives the 
weight of rock per foot of entry length 
that must be held up by the supports: 



P = 2/3 bhy. 



(3) 



A nomographic solution of equation 3 is 
shown in figure 10. The nomogram is used 
as follows: (1) Select the entry width 
on the right side of the X axis; (2) move 
vertically upwards to the appropriate 
rock density curve; (3) move horizontally 
to the left to the appropriate support 
envelope height curve; and (4) move ver- 
tically downwards, and read the weight of 
rock to be supported per foot of entry 
length on the left side of the X axis. 
The correct routing is depicted by the 
three arrows in the figure. Support 
loads for special situations having pa- 
rameters outside the range of the nomo- 
graph can be calculated with equation 3. 

Equation 3 or figure 10 permits the de- 
termination of support loads per foot of 
entry length for various entry widths, 
rock densities, and envelope heights. An 
estimate of envelope height can be ob- 
tained from prior roof falls. Multiply- 
ing this quantity by the spacing between 
supports along the entry gives the total 
weight to be supported by each support. 
Design of the support beam can then be 
determined by reference to the "Manual 
of Steel Construction" (5) or a similar 
steel design manual. 



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100 90 80 7C 6 50 403530 25 20 15 109 8 7 6 5 4 3 5 3 2.5 2 

SUPPORT LOAD, kips/ft of entry length 



1.5 




1 10 



15 20 

ENTRY 
WIDTH, ft 



FIGURE 10. - Nomogram for determining support loads. 



Four different types of beam loadings 
are shovm in figure 11. They include 
concentrated loading, uniform loading, 
uniformly varying loading, and parabolic 
loading. Formulas for calculating end 
reaction, maximum shear, maximum moment, 
and maximum deflection are presented for 
each case. 



rock to be carried by each support. The 
maximum moment to be resisted in terms of 
the total load and beam length is 



M 



5 WL 5 (164,000) (16) 



ma X 



32 



32 



= 410,000 fflb. 



(4) 



SUPPORT SELECTION 

The design example is based on the fol- 
lowing assumptions. A 16-ft-wide entry 
is to be supported. The roof is composed 
of shale rock with a density of 160 lb/ 
ft-'. Support envelope height is esti- 
mated as 24 ft (3b/2), indicating that 
heavy loading is expected. The supports 
will be spaced 4 ft apart along the en- 
try. Parabolic loading of the supports 
by the roof rock (case 4) is assumed. A 
typical yield strength of structural 
steel is 36,000 psi. It is assumed that 
the critical load condition causes yield- 
ing of the section. In other words, the 
failure load is defined when one element 
of the supporting structure has reached 
yield strength of the steel. 

The nomograph of figure 10 gives a sup- 
port load of 41 kips per foot of entry 
length for a 16-ft-wide entry, 160-lb/ft^ 
rock density, and 24-ft-high support en- 
velope. Multiplying this number by the 
4-ft support spacing gives 164 kips or 
164,000 lb as the total weight of roof 



The required section modulus is obtained 
by converting the maximum moment to inch 
pounds and dividing by the yield strength 
of 36,000 psi. 



S = 



M„ 



(410,000) (12) 
36,000 



= 137 in^. (5) 



Referring to the "W Shapes, Properties 
for Designing" section of a steel con- 
struction manual (_5 ) , and using the plas- 
tic modulus (Zj<) column, choose the fol- 
lowing beams as having at least a 137-in^ 
section modulus: 



W 14 X 82, 



W 16 X 77, 



W 18 X 71, 



W 21 X 62. 



Without concern for headroom or clear- 
ance, select the lightest weight section, 
which is the W 21 x 62 beam. The second 
number in the W designation is the beam 
weight in pounds per foot. Pertinent 
properties of the selected beam are 
listed in figure 12. 



12 



W 



R 

End reaction; R = 



W 



Maximum shear; V, 



Maximum moment: M 



W 



WL 



max 



Maximum deflection; fS 



= 0.0 208- 



max 48EI ^ 

Case 1 - c o nc e n t r a t e d load 




Total load: W = 



End reaction: R = 



qL w 



Maximum shear:Vmax~ 



W 



qL*^ WL 



Maximum m o m e n t : M^ a x = T^ = "~5~ 
Maximum d e f I e c t i o n: 6 m a x = 120EI ^ 60EI 
Case 3-uniformly varying load 



A n 

-* L »► 



Total load ; W = qL 



End reaction; R = 



qL W 



Maximum shear; V, 



W 
2 



Maximum moment;Mmax = 
Maximum deflection; '^ 



qJLf_^WL 
8 8 

_ 5 q L^ ^ 5 W L^ 
f^a^' 384EI 384EI 



0.0 13 



WL- 



Case 2-uniform load 

FIGURE 11.. Types of 
CHECKS FOR SUPPORT ADEQUACY 

The selected beam will now be checked 
for the following conditions. 

1. Shear capacity. 

2. Lateral stability. 

3. Deflection, 

4. Localized buckling. 

5. Support length (web crippling). 




Total load: W = 



2qL 



q L w 
End r e a c t i on: R = — -- = — 

q L w 
Maximum s h e a r: V^ a x ~ ""T~~ T 

5qL^ _ 5WL 
32 



Maximum moment:M 



max 



48 



Maximum d e f le c t io n:5 , 



eiqL^ 6 1WL' 



f"^^ 5,760EI 3,840EI 
Case 4-parabolic loading 

beam loading conditions. 

All steel design and review calcula- 
tions are based on the specifications of 
the American Institute of Steel Construc- 
tion. Plastic design methods have been 
used throughout this example. 

Shear Capacity 

The maximum shear on the beam is 



V„,, . f . i^MOO , 82.000 lb. (6) 



13 



ill 



1,375 



+ 25, 



(8) 



'w 



Y 



f 



ZxPlastic section m o d u I u s = 1 4 4 In-' 

d:beam depth=21 in 

tyy:web thick ness=«04 in 

r;radlus of gyration about Y axis=1.77 in 

l:tnoment of inertia about X axis»1,330 in^ 

bfiflange width=8.24 in 

t|:flange t tiic k ness= . 6 1 5 in 

k:distance from outer face of flange to web toe 

of fillet* 1 25 in 
E: modulus of e la s 1 1 c i t y= 2 9 , , 00 psi 

Fyiyield strengfti of steel»36.000 psi 

FIGURE 12. • Pertinent properties for selected 
beam. 

The allowable shear for the selected beam 
in terms of the yield strength (Fy), web 
thickness, and beam depth (see figure 12 
for symbols and values) is 

Va = 0.55 (Fy) (tj (d) 

= 0.55 (36,000) (0.4) (21.0) 

= 166,300 lb. (7) 

Since the allowable shear is greater than 
the maximum shear, this size beam is ac- 
ceptable for the shear loading. 

Lateral Stability 

The critical length for lateral stabil- 
ity is calculated by the formula 



where the yield strength of the steel 
(F ) is used in kips per square inch. 
Substituting in the formula gives 



cr 



= (1.77) 



= HI in. 



1,375 
36 



+ 25 



(9) 



As the beam is 16 ft long, it should be 
braced (struts from beam to beam) on the 
compression flange at the midspan of the 
beam. This lateral bracing will prevent 
buckling of the compression flange. 

Deflection 

The deflection formula (figure 11, case 
d) is 

= 61 WL^ 
•"^x 3^840 EI 

= 61 (164,000) (16)^ (12)3 
3,840 (29,000,000) (1,330) 

= 0.478 = 0.5 in. (10) 

Measurement of beam deflection permits a 
quick check on the condition of the beam. 
The midspan deflection can be measured 
with a pocket tape by stretching a string 
from one support to the other. For exam- 
ple, if 0.25-in deflection is measured, 
the beam still retains approximately 50 
pet of its load capacity. 

Localized Flange or Web Buckling 

Beams are made with different flange 
and web thicknesses and may be subject 
to localized buckling, even though their 
section modulus is adequate for the load. 

Flange thickness is checked with the 
following formula: 



14 



2t, 



< 8.5. 



(11) 



R 



Substituting the selected beam values 
in the formula. 



8.24 



= 6.70 < 8.5; 



2 (0.615) 
beam is acceptable. 



(12) 



The equation for checking web thickness 
assuming no axial load is 



412 



Where the yield strength of the steel 
(Fy) is used in kips per square inch, 
substituting beam values in the equation 



21 
0.4 



412 
= 52.5 < -7^ = 68.7; 



7jh 

beam is acceptable. (13) 
Support Length (Web Crippling) 



This test is to check for localized web 
buckling from the concentrated loading 
that occurs over the supporting posts. 
The appropriate equation is 



0.75 Fy (t„) 



- k. 



(14) 



where N = the required bearing length be- 
tween the beam and its support, in, 

R = the end reaction, lb, 

and t^^ and k are defined in figure 12. 

Substituting beam values into the 
equation, 

82,000 



N = 



0.75 (36,000) (0.4) 
- 1.25 = 6.34. 



(15) 



If a bearing length between the bot- 
tom of the beam and the supporting post 
of less than 6.3 in is used, a stiff- 
ener should be used at the end of the 
beam. This reinforcement can be provided 
by welding plates to both sides of the 
web. 

The selected beam has been checked, us- 
ing plastic theory based upon the recom- 
mendations of the AISC specifications, 
and has been found to satisfy the assumed 
loading conditions. 



SUMMARY 



The major source of injuries appears to 
be handling the steel supports, primarily 
due to their weight and awkwardness. Ac- 
ceptable mechanical methods for quicker 
and safer installation of the heavy steel 
supports in the confining mine environ- 
ment are needed. 

The arch is a more efficient configura- 
tion than the flat crossbar, as the load 
is transmitted as compression rather than 
bending forces. Yielding arches are more 
effective than rigid arches under se- 
vere conditions that produce large de- 
formations. The void space between the 
arch and the strata must be backfilled 



or blocked to provide uniform load- 
ing. Steel supports should be installed 
close to the face 
exposure. 



and shortly after roof 



The load to be carried by steel sup- 
ports can be calculated by assuming a 
parabolic-shaped roof support envelope. 
The actual height of this support enve- 
lope in a particular mine can be esti- 
mated by observing roof falls. A nomo- 
gram is provided for determining support 
loads per foot of entry length for vari- 
ous entry widths, rock densities, and 
support envelope heights. The support 
beam can then be designed by referring to 



15 



any steel construction manual. A design 
example is provided with pertinent equa- 
tions and calculations. Equations are 
provided for checking the selected beam 



for adequacy, with respect to shear ca- 
pacity, lateral stability, deflection, 
localized buckling, and web crippling. 



REFERENCES 



1. Peng, S. S, Coal Mine Ground Con- 
trol. Wiley, 1978, 405 pp. 

2. Hawkins, S. A. Health and Safe- 
ty Analysis on Support Walls. Volume 2: 
Steel Supports Design Criteria: A Sum- 
mary of European Data (contract JO295036, 
Management Eng. , Inc.). BuMines OFR 
121(2)-82, 1980, 61 pp.; NTIS PB 82- 
251968. 

3. Spruth, F. Steel Roadway Supports: 
A Practical Handbook. Collier Guardian 
Co., Ltd., London, v. 2, 1960, 750 pp. 

4. Proctor, R. V., and T. L. White. 
Rock Tunneling With Steel Supports, Com- 
mercial Shearing, Inc., Youngs town, OH, 
1946, 278 pp. 



5. American Institute of Steel Con- 
struction, Inc. Manual of Steel Con- 
struction. 7th ed., 1973, 1200 pp. 

6. Salmon, C. G. , and J. F, Johnson. 
Steel Structures. Harper & Row, 2d ed., 
1980, 945 pp. 

7. McCormac, J. C. Structural Steel 
Design. Harper & Row, 3d ed., 1982, 662 
pp. 

8. Kuzraanovic, B. 0., and N. Willems, 
Steel Design Structures. Prentice-Hall, 
2d ed. , 19 78, 600 pp. 



16 . 

APPENDIX. —EXPLANATION OF SYMBOLS 

A Area 

b Entry width 

bf Flange width 

d Beam depth 

E Modulus of elasticity 

Fy Yield strength of steel 

Y Density of rock 

h Height of roof envelope 

I Moment of inertia about Y axis 

k Distance from outer face of flange to web toe of fillet 

L Beam length 

l(,p Critical length for lateral stability 

Mn,ax Maximum moment 

N Required length between beam and support 

P Weight of rock that must be supported 

q Magnitude of distributed load on beam 

R End reaction 

r Radius of gyration about Y axis 

S Section modulus 

tf Flange thickness 

ty, Web thickness 

V Volume 

Vg Allowable shear 

V^ax Maximum shear 

W Total load 

Zx Plastic section modulus 

6n,ax Maximum deflection 

fiU.S. CPO: 1981-505-019/5068 I N T.- BU.O F M IN ES, P GH., P A. 277 25 



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